The position of a particle moving along the x axis is given by x = 6.0t2 -1.0t3, where x is in metres and t in seconds. What is the position of the particle when it achieves its maximum speed in the positive x direction?
A)24 m
B)12 m
C)32 m
D)16 m
E)2.0 m

Question

Quizplus · Accepted Answer

The velocity is given by the derivative of the position function: v = dx/dt = 12t - 3t^2. The maximum speed in the positive x direction occurs when the acceleration is zero, which is the derivative of velocity: a = dv/dt = 12 - 6t = 0. Solving for t gives t = 2 s. Substituting t = 2 s into the position function x = 6.0t^2 - 1.0t^3 gives x = 16 m.

The Position of a Particle Moving Along the X Axis